It’s neat! To be fair, as a physicist, I did not understand the Legrendre transform essentially until taking convex optimization (where it is known as the Fenchel conjugate).
Many sources, but all of them are reasonable and give a constructive definition that actually explains what it does: we can characterize a function either by its graph, or its supporting hyperplanes (when it is a closed, convex function).
While the observation is almost silly, it has very deep consequences for different characterizations of problems and other constructions!
Many sources, but all of them are reasonable and give a constructive definition that actually explains what it does: we can characterize a function either by its graph, or its supporting hyperplanes (when it is a closed, convex function).
While the observation is almost silly, it has very deep consequences for different characterizations of problems and other constructions!